Maximum likelihood parameter estimation in the three-parameter gamma distribution

Abstract

A successful maximum likelihood parameter estimation scheme for the three-parameter gamma distribution is introduced using the reparametrized distribution function and the predictor-corrector method. As the proposed algorithm can almost always obtain the existing maximum likelihood estimates, it is of considerable practical value. This paper shows that using the reparametrized gamma distribution is superior to the original distribution itself in searching for local maximum likelihood estimates and that the predictor-corrector method proposed in this paper can find all the critical points of the likelihood function in certain parameter domain. The intriguing fact that there exist multiple local maximum points for the likelihood function is illustrated. A Monte Carlo simulation study shows the effectiveness of the proposed method. Only complete data sets are considered in this paper, but the algorithm can easily be applied to censored data.